The relevance of many-body effects, over and above the independent- particle approximation, on the optical properties of semiconductors has been increasingly recognized over the years. Specifically, the collective effect of screening has long been known to be essential to account for the reduction of the electron-hole attraction in an exciton and for the polarization accompanying a single-particle excitation. Only more recently however, it has been possible to give quantitative account of these phenomena by combining Green\'s function techniques of quantum field theory with the description of band structures in terms of localized (molecularlike) orbitals [1-3]. The theory of elementary excitations in crystalline semiconductors with electronic states that are to some extent localized, which has emerged from these efforts, can be considered rather well established by this time. Objective of this paper is to give a pedagogical review of the theoretical framework underlying the calculations of many-particle properties in semi- conductors which are based on the concepts of single- and two-particle ex- citations. Biased by the beliefs that, quite generally, only through detailed knowledge of the theory one can correctly formulate the problems and that, for the specific physical phenomena of interest, the Green\'s functions method provides the very language to describe them, we shall put special emphasis on the working procedures that are important for appreciating the subtleties of the method, but are not commonly described in the literature. For these reasons, results of numerical calculations will be only sketchly presented and references will be given to the original papers for additional details. In particular, when relating theoretical results with experimental quantities, the direct link between the two-particle Green\'s function and the correlation functions of linear response theory will extensively be exploited. It is, in fact, the focus on the correlation functions that renders the Green\'s functions method quite efficient and practical by avoiding the calculation of redundant information.

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